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Chapter 7: Q. 371 (page 732)

Solve each rational function inequality and write the solution in interval notation.

Given the functionR(x)=(x-5)(x-2)find the values of x that make the function less than or equal to 0.

Short Answer

Expert verified

Solution for inequality isx鈭�(2,5].

Step by step solution

01

Step 1. Given Information

The given rational function is denoted asR(x)=(x-5)(x-2).

02

Step 2. Critical point

To find the critical points,

(x-5)=0x=5(x-2)=0x=2

To check the values,

Atx=5,R(x)=03,R(x)=0Atx=2,R(x)=2-50,R(x)=鈭�

When the polynomial function is undefined, the critical point will not add in interval notation.

03

Step 3. Number line

On dividing the number line using critical point,

04

Step 4. Testing of polynomial expression

On testing the sign of polynomial expression and number line sign of factors.

Thus,(x-5)(x-2)鈮�0istrueforx鈭�(2,5].

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